Transformation of Linear Spaces and Linear Operators by Inverse Reversion

This thesis develops a new method for transforming and extending the classes of operators and operands which appear in certain linear operations in such a way that restrictions on the ranges and domains of the operands and on the algebraic manipulation of the operators are reduced and removed. In particular, the method leads to a complete rationalization of the P operators and impulse 'functions' employed by Heaviside, Dirac and others in the analysis of certain linear systems. In this method, the operators A of a primary class K are, in effect, first reversed, forming A*, then inverted, forming A*-1, the inverse reverse of A, and these operators are utilized to effect the remaining transformations and class extensions. The method is therefore epitomized by the phrase inverse reversion.</p

Rock glaciers and mountain hydrology: A review

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In mountainous regions, climate change threatens cryospheric water resources, and understanding all components of the hydrological cycle is necessary for effective water resource management. Rockglaciers are climatically more resilient than glaciers and contain potentially hydrologically valuable ice volumes, and yet havereceived lessattention, even though rock glacier hydrologicalimportance may increase under future climate warming. In synthesising data from a range of global studies, we provide the first compre-hensive evaluation of the hydrological role played by rock glaciers. Weevaluate hydrological significanceover a range of temporal and spatial scales, alongsidethe complex multiple hydrological processes with which rock glaciers can interact diurnally, seasonally, annually, decadally and both at local and regional extents.We report that although no global-extent, complete inventory for rock glaciers exists currently, recent research efforts have greatly elaborated spatialcoverage.Using these research papers,we synthe-sise information on rock glacier spatial distribution, morphometric characteristics, surface and subsurface features, ice-storage and hydrological flow dynamics, water chemistry, and future resilience, from which we provide the first comprehensive evaluation of their hydrological contribution. We identify and discuss long-, intermediate-and short-term timescales for rock glacier storage, allowing a more balanced assess-ment of the contrasting perspectives regarding the relative significance of rock glacier-derived hydrological contributions compared to other water sources.We show that further empirical observations are required to gain a deeper hydrological understanding of rock glaciers, in terms of(i) their genesis and geomorpho-logical dynamics (ii) total ice/water volume; (iii) water discharge; and (iv) water quality. Lastly, we hypothesisethat at decadal and longer timescales, under future climate warming, degradation of ice within rock glaciers may represent an increasing hydrological contribution to downstream regions, and thus in-creased hydrological significance while rock glacier water stores persist.Royal Geographical SocietyNatural Environment Research Council (NERC